"In the words of Eminem, 'It feels so good to be back!!' #OilCity," Jones wrote on his Twitter page.
"Excited to get to wear the Oil drop for another year. Hoping to prove the doubters wrong and help this team return to the 'glory days!'"
In 282 career NHL regular-season games with the Nashville Predators and Oilers, Jones has accumulated 52 goals and 42 assists for 94 points, along with 141 penalty minutes.
He was originally drafted by the Minnesota Wild in the fourth-round (111th overall) of the 2004 NHL Entry Draft.